You are playing a game of dice in the back alley and you sus

You are playing a game of dice in the back alley and you suspect that your opponent is cheating with a loaded die. You take the die and roll it 100 times and count the number of time that each face comes up. The die rolls are: (10, 14, 32, 27, 10, 7) for sides one through six respectively. Conduct a Goodness of Fit test of the hypothesis that the die is fair. What is the Chi Square Statistic of the test?

Question 2 options:

31.26

31.72

31.13

31.59

31.88

31.57

Solution

For a fair die, the probability of each face is 1/6.

Thus, the expected value of each face shoud be

Expected = (16.667,16.667,16.667,16.667,16.667,16.667)

Thus, using

chi^2 = Sum[(O - E)^2 / E]

Then

chi^2 = 31.88 [ANSWER, OPTION 5]